((a)) The indenture trustee shall be authorized—
((1)) in the case of a default in payment of the principal of any indenture security, when and as the same shall become due and payable, or in the case of a default in payment of the interest on any such security, when and as the same shall become due and payable and the continuance of such default for such period as may be prescribed in such indenture, to recover judgment, in its own name and as trustee of an express trust, against the obligor upon the indenture securities for the whole amount of such principal and interest remaining unpaid; and
((2)) to file such proofs of claim and other papers or documents as may be necessary or advisable in order to have the claims of such trustee and of the indenture security holders allowed in any judicial proceedings relative to the obligor upon the indenture securities, its creditors, or its property.
((b)) Each paying agent shall hold in trust for the benefit of the indenture security holders or the indenture trustee all sums held by such paying agent for the payment of the principal of or interest on the indenture securities, and shall give to such trustee notice of any default by any obligor upon the indenture securities in the making of any such payment.